What Is An Upper Limit?

Details What Is An Upper Limit? What Is An Upper Limit?

Mar 2008

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2008head...10.0302k&link_type=abstract

American Astronomical Society, HEAD meeting #10, #3.02

Mathematics

Probability

Scientific paper

When a known source is undetected at some statistical significance during an observation, it is customary to state the upper limit on its intensity. This limit is taken to mean the largest intrinsic intensity that the source can have and yet remain undetected. (Or equivalently, the smallest intrinsic intensity it can have before its detection probability falls below a certain threshold.)
Note that this definition differs from the concept of the parameter confidence bounds that are in common usage and are statistically well understood. This similarity of nomenclature has led to a confusing literature trail.
Here we describe the upper limit, or the detection limit, as used by astronomers in a statistically coherent fashion. We show that it follows naturally from the calculation of the statistical power and describe examples to illustrate how it works and how to calculate it in real world cases (see also Aldcroft et al., this conference).
This work was supported by the Chandra X-ray Center NASA contract NAS8-39073 and NSF grant DMS 04-06085.

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